Questions tagged [renormalization]
This tag is for questions which relates with the renormalization, an ensemble of techniques which serves to treat the infinities which appear in quantum field theory or statistical mechanics. Renormalization procedures are based on the requirement that certain physical quantities (such as the mass and charge of an electron) equal observed (experimental) values.
656
questions with no upvoted or accepted answers
17
votes
1
answer
505
views
Renormalisation and the Fisher-Rao metric
The renormalisation group (I'm talking about classical, statistical physics here, I'm not familiar with field theory too much) can be thought of as a flux in a space of possible Hamiltonians for a ...
- 3,279
15
votes
0
answers
235
views
About variational methods, renormalization and $a$, $c$-theorems
Variational approximation
Variational methods are an important technique, frequently applied for the approximation of complicated probability distributions, with the applications in statistical ...
- 4,883
12
votes
1
answer
2k
views
LSZ reduction theorem derivation in Weinberg QFT
When deriving LSZ reduction theorem Weinberg in his QFT book have assumed n-point generalized Green functions,
$$
G(q_{1},...,q_{n}) = \int d^{4}x_{1}...d^{4}x_{n}e^{-i\prod_{i =1}^{n}q_{j}x_{j}} \...
- 6,564
12
votes
0
answers
2k
views
How do we know for sure a theory is non-renormalizable?
In quantum field theory, we are looking for a Lagrangian that is, amongst other, renormalizable. But how do we determine whether or not a theory is renormalizable? Is this purely done by power ...
- 5,228
10
votes
0
answers
632
views
$d=2$ pole argument of quadratic divergences in Peskin & Schroeder's book
Q1:
My question is, in the context of dimensional regularisation(DREG, in dimension $d$), why do they mention the absence of $d=2$ pole in the gauge theory cases[1], whereas the $d=2$ pole is not ...
- 1,161
10
votes
0
answers
221
views
Are irrelevant terms in the Kahler potential always irrelevant, even at strong coupling?
I've been reading about the duality cascade in Strassler's TASI '03 lectures (hep-th/0505153). He reminds us of the non-renormalization theorem theorem for the superpotential so that the beta ...
- 457
10
votes
0
answers
802
views
Instantons and Borel Resummation
As explained in Weinberg's The Quantum Theory of Fields, Volume 2, Chapter 20.7 Renormalons, instantons are a known source of poles in the Borel transform of the perturbative series. These poles are ...
- 1,776
9
votes
0
answers
394
views
Dimension of gamma matrices in dimensional regularization
When performing loop integrals in theories containing Dirac fermions, one almost always confronts terms of the form
$$\text{Tr}\left[\gamma^{\mu_1}\cdots\gamma^{\mu_n}\right].$$
For instance, in $d$ ...
- 8,490
9
votes
0
answers
682
views
Effective Field Theory (EFT) decoupling top
The decoupling theorem of Appelquist-Carazzone says that if you want to decouple a particle, the low energy resulting theory need to be renormalizable. You can't do that for the top, because you break ...
- 346
9
votes
0
answers
694
views
Drawing the RG flow diagram
In real-space renormalization group how does one find the complete RG flow exactly, (not schematically)? I understand it needs to be done on a computer. For example, I have the ising model on a ...
user21476
8
votes
0
answers
126
views
Uniqueness of high temperature RG fixed point
Given a $\phi^4$ theory in $d<4$
$$S_{\Lambda} = \int d^dx \left[\frac{1}{2}(\partial_i \phi)^2 + \frac{1}{2} \mu_0^2 \phi^2 + \Lambda^{d-4} \tilde{g}_0 \phi^4 \right]\,,$$
the corresponding RG ...
- 81
8
votes
0
answers
268
views
Fisher exponent and fractal structure
In the context of critical phenomena, there are several critical exponents commonly used to characterize the singular behaviour at the point of phase transition. The Fisher exponent $\eta$ is defined ...
- 498
8
votes
0
answers
187
views
Low-energy effective actions in string theory: agreement between beta-function vs. scattering-based derivations?
In string theory, in my limited understanding, starting with the worldsheet theory, we have at least two methods for deriving the low-energy effective action on the target spacetime. We can either
...
- 684
8
votes
0
answers
357
views
Renormalization group approach to renormalization
Given a $n$-point bare Green function in a massless asymptotically free theory, we have that the following limit exists and is finite
\begin{equation}
\lim_{\Lambda\rightarrow\infty} Z^{-n/2}(g_0,\...
- 2,263
8
votes
0
answers
382
views
Understanding the Renormalization Group for Entanglement Entropy
I'm trying to understand the renormalization group (RG), and in particular, how it is used to study entanglement entropy (EE) and c-theorems in quantum field theory (QFT). But I'm having trouble with ...
- 81